In this talk we concentrate on relativistic hypercomputation which amounts to using the special features of general relativity (GR) for computing beyond the Turing limit. In more detail:
We use special features of GR for designing a possible physical experiment which enables the experimenting civilization to compute some function which is not Turing computable. We discuss two approaches to relativistic hypercomputation. The first approach has already been outlined in our earlier papers and presentations while the second one is relatively new but was discussed in works of Gergely Szekely.
The first approach is based on rotating huge black holes whose spacetime is known as Kerr-Newman spacetime (known also as Kerr-Newman wormholes). The mathematics of this spacetime is related to Gödel's rotating universe known as Gödel's spacetime. There is overwhelming astronomical evidence for the existence of such black holes.
The second approach is based on Lorentzian wormholes as they are discussed in, e.g., Wikipedia. In this approach we rely on wormhole-theory elaborated in works on relativist Igor Novikov and his school. An advantage of the second approach is that in these wormholes spacetime curvature is negative. Therefore wormholes act like gravitational defocussing lenses while Kerr-Newman black holes (Kerr-Newman WH's) act like gravitational focussing lenses. Hence, the stability problems showing up (and solved with some effort) in the first approach do not show up in the second one. In the talk we will compare the relative merits of the two approaches. E.g., we will see that wormholes have advantages in complexity issues. "Wormhole computing" can attack more complex problems than black hole computing.
In passing we note that the second approach was made possible, roughly, by the relatively recent discoveries of, e.g., the (never ending) accelerated expansion of the Universe and the violations of the various energy conditions, which imply that negative curvature, hence negative energy, is possible in our Universe after all.